Elementary proofs of grothendieck theorems for completely bounded norms

Oded Regev, Thomas Vidick

Research output: Contribution to journalArticlepeer-review


We provide alternative proofs of two recent Grothendieck theorems for jointly completely bounded bilinear forms, originally due to Pisier and Shlyakhtenko (Grothendieck's theorem for operator spaces, Invent. Math. 150(2002), 185-217) and Haagerup and Musat (The Effros-Ruan conjecture for bilinear forms on C*-algebras, Invent. Math. 174(2008), 139-163). Our proofs are elementary and are inspired by the so-called embezzlement states in quantum information theory. Moreover, our proofs lead to quantitative estimates.

Original languageEnglish (US)
Pages (from-to)491-506
Number of pages16
JournalJournal of Operator Theory
Issue number2
StatePublished - 2014


  • Bilinear form
  • Completely bounded norm
  • Grothendieck inequality
  • Quantum information theory

ASJC Scopus subject areas

  • Algebra and Number Theory


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